Degrees in oriented hypergraphs and Ramsey \(p\)-chromatic number
type: Item
instance of: scholarly article
title: Degrees in oriented hypergraphs and Ramsey \(p\)-chromatic number
zbMATH Open document ID: 1252.05141
author: Yair Caro
author: Adriana Hansberg
published in: The Electronic Journal of Combinatorics
publication date: 2012-10-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1112.3302
full work available at URL: v19i3p16
review text: Summary: The family \(D(k,m)\) of graphs having an orientation such that for every vertex \(v \in V(G)\) either (outdegree) \(\deg^+(v) \leq k\) or (indegree) \(\deg^-(v) \leq m\) have been investigated recently in several papers because of the role \(D(k,m)\) plays in the efforts to estimate the maximum directed cut in digraphs and the minimum cover of digraphs by directed cuts. Results concerning the chromatic number of graphs in the family \(D(k,m)\) have been obtained via the notion of \(d\)-degeneracy of graphs. In this paper we consider a far reaching generalization of the family \(D(k,m)\), in a complementary form, into the context of \(r\)-uniform hypergraphs, using a generalization of Hakimi's theorem to \(r\)-uniform hypergraphs and by showing some tight connections with the well known Ramsey numbers for hypergraphs.
Mathematics Subject Classification ID: 05C55
Mathematics Subject Classification ID: 05C65
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 6098358
zbMATH Keywords: oriented hypergraphs
zbMATH Keywords: Ramsey \(p\)-chromatic number
zbMATH Keywords: \(d\)-degenerate hypergraph
zbMATH Keywords: Ramsey numbers
zbMATH Keywords: chromatic number
MaRDI profile type: Publication
arXiv ID: 1112.3302
description: scientific article; zbMATH DE number 6098358